Dividing Rational Numbers Section 2.5

Objectives Divide rational numbers. (NS 1.2) Simplify numerical expression by applying inverse properties of rational numbers. (AF 1.3)

Reciprocal Two numbers whose Words to Know Reciprocal Two numbers whose product is 1. Also called the multiplicative inverse.

To divide fractions… Find the reciprocal of the second fraction. Multiply the numerators. Multiply the denominators. Simplify

Let’s Try One… 1 5 Find the reciprocal of the second fraction. Simplify Multiply the numerators. Multiply the denominators. 2 6 3 1 6 2 5 1 3 5

Let’s Try One… 1 3 4 Make the mixed number an improper fraction. Find the reciprocal of the second fraction. Simplify Multiply the numerators. Multiply the denominators. 2 4 2 3 9 4 2 3 1 1 6 6 = 1

Let’s Try Another… 3 2 Find the reciprocal of the second fraction. Simplify Multiply the numerators. Multiply the denominators. 4 1 3 1 4 2 3 8

How do you divide fractions?

Now You Try… 1 2 3 4

…A Few More 5 6 7 8

Dividing Decimals Find 0.65 ÷ 0.25 2 .6 25 )65.0 - 50 15 –150 0.25 )0.65 0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 2 .6 25 )65.0 - 50 15 –150 Then divide as a whole number. The answer is reasonable.

Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. 5.25 for n = 0.15 n 5.25 n 0.15 = Substitute 0.15 for n. 0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer. 0.15 )5.25 35 15 )525 - 525 When n = 0.15, = 35. 5.25 n

Understand the Problem 1 2 A muffin recipe calls for cup of oats. You have cup of oats. How many batches of muffins can you bake using all of the oats you have? 3 4 The number of batches of muffins you can bake is the number of batches using the oats that you have. List the important information: 1 Understand the Problem The amount of oats is cup. One batch of muffins calls for cup of oats. 12 34

2 Make a Plan Set up an equation.

Let n = number of batches. Solve 3 Let n = number of batches. 12 34 = n ÷ 34 21 = n • 64 , or 1 = n 12 You can bake 1 batches of the muffins. 12 Look Back 4 One cup of oats would make two batches so 1 is a reasonable answer. 12

Lesson Quiz 89 Divide. 5 6 1 2 –1 1. 2 ÷ –1 2. –14 ÷ 1.25 –11.2 3. 3.9 ÷ 0.65 6 112 x 4. Evaluate for x = 6.3. 17.7 5. A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)? about 182